Crystallographic–Morphological Connections in Star Shaped Metal–Organic Frameworks

The symmetry of a crystal’s morphology usually reflects the symmetry of the crystallographic packing. For single crystals, the space and point groups allow only a limited number of mathematical descriptions of the morphology (forms), all of which are convex polyhedrons. In contrast, concave polyhedrons are a hallmark of twinning and polycrystallinity and are typically inconsistent with single crystallinity. Here we report a new type of structure: a concave polyhedron shape single crystal having a multidomain appearance and a rare space group (P622). Despite these unusual structural features, the hexagonal symmetry is revealed at the morphological levels.


Preparation of the crystals: CSTAR-NO3 and CSTAR-SO4
The metal salt (Cu(NO3)2•3H2O: 5.0 mg, 21 mmol or CuSO4: 5.0 mg, 31 mmol) was dissolved in DMF (1.6 mL for CuSO4; 1.1 mL for Cu(NO3)2•3H2O). A mixture of CHCl3 (1.0 mL) and DMF (2.0 mL) in a glass vial (20 mL) was sonicated (33-40 KHz frequency) for 1.5 h in an ice bath. Subsequently, this solvent mixture was used immediately to dissolve AdDB (3.0 mg, 3.5 mmol). The solution of AdDB and 1.0 mL of the solution of the metal salt were mixed in a glass pressure tube (the final concentrations of AdDB and the metal salt were 0.9 mM and 1.8 mM, respectively). Then, the tube was sealed and heated for 48 h in an oven at 105 o C. Subsequently, the temperature of the controller was decreased every hour by 10°C. CSTAR-NO3 was isolated as a green powder by centrifugation, washed with ethanol and re-dispersed in 1.0 mL ethanol. CSTAR-SO4 appeared both as green crystals at the bottom of the tube and as a greenish powder. Powder X-ray diffraction (PXRD), thermogravimetric analysis (TGA), elemental analyses has been provided in the supporting information (Figure S12-S13, Table S3).

Scanning electron microscopy (SEM)
SEM measurements were performed using HRSEM ULTRA-55 ZEISS instruments at an EHT voltage ranging from 1-1.5 kV. Images were collected in secondary electron mode by using an Everhart-Thornley detector. Samples of CSTAR-NO3 were prepared by drop-casting a dispersion in ethanol on a silicon substrate. Two sample-preparation procedures were used on a carbon tape covering the SEM stub for the imaging of CSTAR-SO4: (a) the reaction mixture was drop-casted and then the solvent was allowed to evaporate, (b) the reaction mixture was drop-casted on a microscope slide, then dried, and the residue was washed with ethanol, dispersed in ethanol and drop-casted on the carbon tape.

Light microscopy images
Light microscopy images were obtained with Nikon's Eclipse E600 and Nikon Eclipse LV100ND microscopes at 20X magnification. The latter microscope is equipped with DeltaPix 2001DeltaPix -2022 software that allows for extended focus imaging.

Powder X-ray Diffraction (PXRD)
The PXRD measurements were performed in reflection geometry by using a TTRAX III (Rigaku, Japan) diffractometer. The diffractometer is equipped with a rotating Cu anode operating at 50 kV and 200 mA. A bent graphite monochromator and a scintillation detector were aligned in the diffracted beam. θ/2θ scans were performed under specular conditions in the Bragg-Brentano mode with variable slits. The MOFs dispersion was drop casted on a silicon plate and allowed to dry at the air before the measurement. PXRD spectra were collected from 5 to 25 degrees with step size of 0.025 degrees.
These experimental PXRD patterns were analyzed by using Jade 2010 software (Materials Data, Inc.).
The lattice parameters were refined using the Whole Pattern Fitting/Rietveld refinement module of Jade 2010.

Single Crystal X-ray (SXRD)
SXRD data were collected both at the synchrotron source (ESRF ID-29) of the European Synchrotron Radiation Facility (ESRF) and using home-lab Rigaku XtaLab Pro or Synergy diffractometers.
The crystals were placed in Hampton Paratone oil, mounted on a MiTeGen loop and plunged into liquid nitrogen to flash freeze. The data were collected at 100 K with Oxford Cryostream. The crystals analyzed at the synchrotron were transported frozen in a Taylor-Wharton CX100 dry shipper. Data collection and reduction for the synchrotron ID-29 data were done using MXCube, and the EDNA automated data processing pipeline with XDS. The structures were solved by direct methods using SHELXT implemented with the Olex2 software GUI. S2 The structures were refined by full-matrix least-squares methods on F 2 with SHELXL. All nonhydrogen atoms were refined with anisotropic displacement coefficients. Hydrogen atoms were placed in calculated positions, assigned isotropic displacement coefficients, U(H) = 1.2U(C) or 1.5U (Cmethyl), and their coordinates were allowed to ride on their respective carbons.
Data collection, reduction and analysis for the XtaLab Pro laboratory data were performed with the CrysAlisPro software package (version 1.171.39.22a, Rigaku OD, 2018). Data collection, reduction and analysis for the Synergy laboratory data were performed with the CrysAlisPro software package (version 1.171.40.80a, Rigaku OD, 2018). The crystal structures were solved by direct methods using SHELXT 2016/4. All non-hydrogen atoms were further refined by SHELXL with anisotropic displacement coefficients. Hydrogen atoms were placed in calculated positions and refined in riding mode on the respective carbon atoms. The Platon SQUEEZE protocol was applied for all the structures.
Mercury CSD 3.10.2 and PLATON software were used for graphics. S3 The crystallographic data and refinement parameters are summarized in Table S1. All crystals have the same rare space group (P622). There are 43 structures with this space group in the database of the CCDC of which 26 have been reported by us. S4-S7 The Ewald sphere's projections were produced by CrysAlis Pro from data sets collected on the Rigaku XtaLab Pro or Synergy systems. These home-laboratory system generators have microfocus Xray tubes with beams approximately 100 m in cross-section; such a beam is large enough to expose the entire crystal simultaneously so that the diffraction data shown plotted in the Ewald spheres is from all the sections of the stars. The Cumulative Intensity statistics were plotted within Olex2. S8 The Laue symmetry statistics and twinning analysis were produced in the XPREP module of SHELX. Details of the crystal structure analysis are reported in the table below.

Indexing of the facets and twinning analysis
The stellate crystals on the Rigaku Synergy or Synergy R were measured and the data were fully processed with CrysAlis PRO 1.171.40, software package (Rigaku OD, 2018). Prior to the X-ray measurement, a 360º video of the mounted crystal was taken for absorption corrections and crystal morphology determination. The approximate magnification of this video system is x450, allowing us to clearly view the crystal (Figures 4, S6 and S7). The video camera of XtaLab Pro is unfortunately of insufficient magnification for this purpose. After the unit cell and space group were determined and the structure solution completed (with Shelxl and Shelxt as implemented in Olex2 Gui), the prerecorded video frames were used for crystal face indexing routine. The unit cell axes vis-à-vis the crystal were determined (Figures 4, S6 and S7). The crystal shape routine of CrysAlis Pro allows for the placement of the best planes the crystal faces, and the approximate Miller indices (hkl) of the faces were indexed where the estimated low integer hkl option was used. It should be noted that the program routine does not allow for the drawing of the unexpected re-entrant angles. Some faces were obscured by the loop or by the meniscus of the cryoprotectant oil. The best planes were identified for each of the faces, where possible. The star morphology appears to comprise vicinal faces that cause deviation from the traditional 1 st -order hexagonal prism. In our case, as in other 1 st -order prisms, the unit cell axes emerge from the vertices between the two prism faces and the Miller indexes; S9 if it were not for the concavity, the faces The existence of the unusual star-shaped crystal combined with a rare, high-symmetry space group raised suspicions of possible crystal twinning. By definition, 'a twin consists of two or more single crystals of the same species but in different orientations. S10 The twin components are grown together in a shared surface called the composition surface or twin interface.
The twinning of crystals, on the macroscopic scale, sometimes manifests as the presence of reentrant crystal angles. S11 When the twinning interfaces are not parallel to each other then they develop as cyclic twins, which can resemble stars. However, the presence of morphological irregularities is in itself not a sufficient indicator. While concave crystal faces do not always indicate twinning, it is certainly a warning sign. S10 On the atomic level, twinning, as with other crystal imperfections, might manifest as certain pathologies such as split reflections and deviation from the expected intensity statistics of diffraction data. S12 However, some forms of twinning can be particularly difficult to determine and not evident until full data sets are analyzed. In particular, merohedral twinning is a type of twinning where the lattices of two or more distinct domains coincide exactly. S13 As the real space lattices coincide, the reciprocal lattices of the domains will exactly overlap and the resulting diffraction pattern will appear normal. This type of twinning can occur in space groups of high symmetry, e.g., tetragonal, trigonal, hexagonal or cubic, where more than one Laue symmetry is possible. In such cases, the additional rotational symmetry operator of the twinning exactly superimposes parts of the diffraction pattern, causing the appearance of higher symmetry, i.e., the twinning adds symmetry. The true Laue symmetry (point symmetry) of the crystal is lower than that of the lattice. S14 The hexagonal space group P622 can be a result of the merohedral twinning of the lower symmetry trigonal space group P321. Therefore, it is imperative for our analysis that this possibility be checked and definitively confirmed or denied. As explained above, since merohedral twinning will not be evident from the diffraction pattern, the intensity distribution of the complete data set needs to be examined. S15 One such widely used analysis involves the identification of twins from intensity statistics. The values of the <|E2-1|> can be plotted and are known to differ for centrosymmetric vs. noncentrosymmetric structures. The theoretical statistical value for centric structures is 0.938, S11 and that of acentric structures 0.736. Twinning results in a diffraction pattern of higher symmetry and yields a hypo-non-centrosymmetric intensity distribution. S16 The cumulative distribution function N(z) gives the fraction of reflections whose relative intensities are less than z, where z is the normalized reflection intensity obtained by dividing each individual measurement by the average value for its resolution shell. S10 When the plot of the cumulative intensity distribution N(Z) for acentric and centric data is plotted, the shape of the plot is a diagnostic. The plot for an un-twinned crystal appears exponential due to the existence of a small number of very weak or very strong reflections, while for a twinned crystal, the plot appears sigmoidal. The sigmoidal shape arises because a portion of the non-equivalent reflections in a twinned crystal will overlap exactly; S17 some of the very strong reflection intensities become averaged with very weak reflections and thus the distribution of reflection intensities N(z) will vary from the theoretical. S18 The cumulative intensity test for star-shaped crystals CIF v440 (CCDC 2117030) and CIF v339 (CCDC 2009649) was calculated in the Olex2 software package and are presented in Figure 3B. The plots clearly show the exponential shape indicative of un-twinned crystals.

Laue analysis
Perfect twinning and the additional twin laws can result in a diffraction pattern and space group with a higher apparent symmetry than the true crystal symmetry. Twinning can also be determined by comparing the Rint values of the true Laue group with those of the apparent Laue group. The Rint (as calculated in Shelx XPREP) will be lower for the true space group. The results of this analysis are shown below Figure 3C. As can be seen, in all the cases, the Rint for the high symmetry 622 is lower than that of the lower symmetry Laue group. This indicates that the higher symmetry of group P622 is indeed true and not an artifact of twinning in lower symmetry. Combined with the results of the cumulative intensity plots, we are confident that our unusual stellate crystals are single.